How to Create and Interpret Energy Diagrams

Roshni Desai, Fall 2023

The Main Idea

Energy diagrams are tools used to analyze a system's energy and motion with respect to a scalar variable like position or time. They are typically used to represent the kinetic and potential energy within a system, in addition to a horizontal line that depicts the total mechanical energy of the system.

To draw the energy graph of a system, the following method should be used:

1. Determine if the potential energy is attractive or repulsive
   • For example, gravitational potential energy is attractive since it draws objects to the surface of the Earth [math]\displaystyle{ \left(U_g \lt 0\right) }[/math].
   • Electric potential energy for charges with the same sign is repulsive, since like charges repel [math]\displaystyle{ \left(U_e \gt 0\right) }[/math].
2. Analyze whether the system is bound, unbound, or at escape speed to determine the location of the total energy line
   • Bound System: A system in which the total energy is negative
     • [math]\displaystyle{ E = K + U \lt 0 }[/math]; horizontal line below the x-axis

A Computational Model

Vpython is great for modeling this concept. Using vpython, we can model many different systems that have kinetic and potential energy. We can model a spacecraft orbiting the Earth, and we can create graphs to display the kinetic, potential, and kinetic+potential energies of this system. See this code for how to do this!

[Sample Vpython code:https://trinket.io/glowscript/4010e21bc3]

Examples

Difficult

creating energy graphs for different situations

Connectedness

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2. How is it connected to your major?
3. Is there an interesting industrial application?

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